Multiplication and Division Concepts and Problem Solving

Multiplying and Dividing Decimals

The multiplication division process is a simple step-by-step format used daily in all fields of Mathematics. The multiplication and division of decimals represent the fraction of a number and taking ten as the base of the decimal system of numbers. Point differentiates or decimal notations is an integer part extracted from the part of a fraction. Decimals can undergo addition, subtraction, multiplication, and division. Multiplication and division processes are easier to use with decimals as compared to addition and subtraction. These functions are normally used in computational platforms and tasks.

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Multiplication of Decimals

In normal multiplication, the numbers indicate also the addition of the number 20 twice. Similarly, this can be applied to decimals as well. Taking the example of 0.22 x 2 = 0.22 + 0.22, the multiplication of whole numbers and the multiplication of decimal numbers go hand-in-hand.  Some simple steps used in the multiplication of decimals are provided below with an example.

Example of Multiplying Decimals

Let’s take the following example to understand how multiplication of decimals is done.

Let us consider the multiplication of two numbers, 4.42 and 2.

Step 1:

Count the total number of digits to the right of the decimal point in both numbers provided. We notice that in 4.42, to the right of the decimal point there are two digits and 4 is a whole number. Therefore, the total number of digits to the right of the decimal is 2.

Step 2: 

Without considering the decimal point,  multiply the numbers found.

442 x 2 = 884 

Step 3:

After multiplication, add the decimal point two places to the right of the answer calculated. 

Division of Decimals

The division of decimals is almost similar to the multiplication of decimals. When dividing a decimal directly, it can be confusing where to place the decimal point. But, with a little practice, one can use the same trick of multiplying decimals with ease. When dividing the decimal as a numerator with a whole number as a denominator of two given numbers, it is easier to obtain a result. 

Examples of Dividing Decimals By Decimals

There are two methods used to divide a given set of decimal numbers. Let us consider the numbers given below, to understand the mechanism of dividing decimals. 

Divide the following decimals 0.398 by 0.20.

Method 1:  

Conversion of the decimals to whole numbers by multiplying each with a common factor to make the denominator one. It is important to note that the denominator has to always be a whole number for the division to take place.

0.398 ÷ 0.20 = \[\frac{0.398}{0.20}\] = \[\frac{0.398 \times 5}{0.20 \times 5}\] = \[\frac{1.99}{1}\] = 1.99

(Multiply both the numerator and denominator by 5)

Method 2:  

Another method to use is to convert the decimal numbers into whole numbers. This can be done by multiplying with numbers having powers of 10 (10, 100, 1000, etc.).

Let us take the above example and count the number of digits right to the decimal point in the denominator.

The denominator is 0.20 and the number of digits right to the decimal point is 2.

0.398 ÷ 0.20 = \[\frac{0.398}{0.20}\]

• The power of 10 is taken common depending on the number of digits present to the right of the decimal point.( 102 = 100)

• Multiply both numerator and denominator by 100.

0.398 ÷ 0.20 = \[\frac{0.398 \times 100}{0.20 \times 100}\] = \[\frac{39.8}{20}\] = 1.99

Multiplying and Dividing Decimals Using 10, 100 and 1000

We have read that decimals are a form of expression fractions having their base as 10. Let us consider a couple of examples with fractions of decimals having the base of 100 and 1000.  Some rules applied for multiplication and division of decimal numbers by 10, 100, and 1000 are as follows: